Ideal Answers to Chapter 12 Questions (Suppressor Variables)
QUESTION 12.1a. There was no correlation between how many anagrams people thought others solved
and how much they paid themselves, r (25) = -.05, p = .814. However, there was a sizable correlation
between how many anagrams people thought they solved and how much they paid themselves, r (25) =
.62, p < .001. The more anagrams these students thought they solved the more they paid themselves.
QUESTION 12.1b. A simultaneous multiple regression analysis predicting self-pay from both the number
of anagrams people thought they solved and the average number they thought others solved revealed
that both predictors were significantly related to self-pay. First, controlling for how many anagrams
people thought others solved, the more anagrams people thought they solved the more they paid
themselves, β = .93, equivalent t (24) = 6.05, p < .001. Second, controlling for how many anagrams
people thought they solved, the more anagrams people thought others solved, the less they paid
themselves, β = -.57, equivalent t (24) = -3.67, p = .001. This second variable seems to be a suppressor
variable because it had no zero-order association with self-pay. From the perspective of Festinger’s
(1958) social comparison theory, it makes sense that, all else being equal, people might pay themselves
more if they think others have done poorly and less if they think others have done especially well. In
other words, it is not merely our performance in isolation that matters but our performance relative to
the performance of others. If Zeke thinks he solved 18 of 20 anagrams but thinks everyone else did the
same, he may not be inclined to pay himself a lot. But if he thinks his score of 18 was well above the
mean score of most other students, he may be convinced that his special performance deserves some
special compensation.
The reason why perceived performance of others was a suppressor variable is that people’s perceptions
of how others did were so strongly correlated with their perceptions of how they did (a form of
projection?), r (25) = .56, p < .001. So, for example, the belief that others solved very few anagrams
tended to co-occur with the belief that participants themselves solved very few anagrams. This second
belief (roughly, “I didn’t do well.”) seems to have masked or suppressed the true effect of thinking other
people sucked at the anagram task. The converse would have been true, of course, for believing that
others did well. Any tendency for people to pay themselves less based on this belief was erased by
people’s beliefs that they, too, solved a lot of anagrams.
QUESTION 12.2a. There was no correlation between income and voting behavior, r (48) = .03, n.s. That
is, poorer versus wealthier people did not differ in their likelihood of voting for Bush (in these
hypothetical data). Not surprisingly, political party was correlated with voting behavior; Republicans
were more likely than Democrats to report voting for Bush, r (48) = .37, p = .009. Finally, the higher
people scored on the measure of fundamentalism, the more likely they were to vote for Bush (recall
that lower scores on the voting measure correspond to a vote for Bush), r (48) = -.67, p < .001.
QUESTION 12.2b. A simultaneous multiple regression analysis revealed that after controlling for both
political party affiliation and degree of fundamentalism, income is uniquely associated with voting
behavior, β = -.22, equivalent t (45) = -2.16, p = .036. All else being equal, wealthier people are more
likely to vote for Bush. The standardized regression coefficients for political party changed were more
consistent with the zero-order correlation involving political party; it was β = .29, equivalent t (45) =
2.91, p = .006. After controlling for income and degree of religious fundamentalism, Republicans were
more likely to vote for Bush. Finally, after controlling for income and political party, there was still a
strong association between degree of religious fundamentalism and voting for Bush, β = -.70, equivalent
t (45) = -6.79, p < .001. Controlling for income and political party, fundamentalists were much more
likely to vote for Bush.
By consulting the original set of correlations among these variables it is possible to see why income was
a suppressor variable. All else being equal, poorer people tend to vote Democratic. However, all else is
not equal. Poorer people are much more likely to be fundamentalists, and the data show that
fundamentalists were much more likely to support Bush rather than Kerry. However, within a given level
of fundamentalism, the poorer people are, the more likely they were to vote for Kerry (the Democratic
candidate).
QUESTION 12.3a. The correlations between homicides rates across nations and the four nation-level
predictor variables appear in Table 8.1.
Table 8.1 Four Potential Correlates of Homicides Rates Across 120 Countries
Predictor
r
n
p
GDP per capita
-.27
115
.004
Percent of pop. aged 14 and under
.23
116
.013
Number of prisoners per capita
.18
120
.051
Freedom House Human Rights Ratings*
.01
120
.956
.
* Note. To facilitate ready interpretation, human rights ratings were rescored so that higher scores indicate
greater human rights, by subtracting the original 1-7 Freedom House scores from 8.
As shown in Table 8.1, wealthier nations (as defined by GDP) had lower homicide rates than poorer
nations. Further, countries where a higher percentage of the population was younger than 15 had higher
homicide rates. If one generously considers p = .051 significant, it also appears that countries that have
higher incarceration rates have more homicides (perhaps because crime often leads to incarceration).
Finally, there was no correlation between human rights and homicide rates. Murder rates were apparently
very similar in countries with poor human rights records and countries with strong human rights records.
QUESTION 12.3b. To check and see if a suppressor variable was at work, I conducted a simultaneous
multiple regression in which I predicted homicide rates from all four of the predictor listed in Table 8.1.
Table 8.2 summarizes the results of this analysis.
Table 8.2 Standardized Regression Coefficients for Four Predictors of Homicides Rates Across 120
Countries
Predictor
β
t
p
GDP per capita
-.26
-2.15
.034
Percent of pop. aged 14 and under
.22
1.80
.075
Number of prisoners per capita
.23
2.51
.014
Freedom House Human Rights Ratings*
.24
2.22
.029
.
The n for all variables was 111 because I accepted the default of listwise deletion of cases with any missing
variables. When I re-ran the analysis and accepted mean substitution for all missing data (leading to n =
120) the results changed very little, and the positive effect of human rights ratings remained significant.
The simultaneous multiple regression analysis confirmed that the association between GDP and homicide
rates holds up while controlling for the other three predictor variables. All else being equal, wealthier
countries have lower homicide rates. Presumably, many features of wealthy countries discourage murder,
ranging from more and better trained police officers to greater rule of law and greater availability of street
lamps, telephones, or personal safety devices (including things as basic as locks for doors and windows).
There was also a marginally significant unique effect of the percent of people aged 14 or under in each
country. This marginally significant effect suggests, albeit very tentatively, that all else being equal,
countries with a higher percentage of young people have higher homicide rates. This is consistent with the
idea that homicide, like other crimes, is a young person’s game. However, it seems at least as plausible
that this variable is a proxy for the kind of difficult living conditions (rapid population growth, high infant
mortality) that tend to promote crime.
The number of prisoners per capita also held up as a unique predictor. All else being equal, homicide rates
are higher in countries where more people are incarcerated. This unique effect could obviously reflect
mean that more murders (and perhaps other crimes) lead to more incarcerations or that conditions that
promote incarceration also promote murder. Though less plausible, the finding could even mean that
putting more people in jail somehow contributes to higher murder rates.
Finally, the most interesting finding is that after controlling for the other three predictors (wealth, youth and
incarceration rates), countries where people have more human rights have higher homicide rates. This
may mean that, all else being equal, greater personal freedom provides people with greater opportunities to
commit crimes. In Singapore, for example, people enjoy a high standard of living but do not enjoy the same
kind of personal freedoms most Americans and Western Europeans enjoy. According to these data, the
murder rate in Singapore (0.5 people per 100,000) is less than 1/10 the rate observed in the U.S. (5.5.
people per 100,000). This variable is a suppressor variable, of course, because it had no zero order
correlation with homicide rates. A look back at the correlation matrix involving all five variables suggests
two reasons why this positive association may have been masked. Countries where people have more
human rights tend to have much higher GDPs (r = .50) and much lower percentages of young people in the
population (r = -.51). Of course, wealthy countries that do not have a surplus of very young people tend to
have lower murder rates, and so these two variables collectively could have masked the positive effect of
having many human rights on homicide.
Having said all that, I should add that I would be a little more comfortable saying that there is a positive
unique association between human rights and murder rates if it held up when we only controlled for either
one of these variables at a time. When I tried various versions of the regression model, the positive
(suppressor) effect for human rights only held up when I controlled for both GDP and percent of population
aged 14 and under. I’d like to see this effect replicated for a different time period before I place full
confidence in it.